An Efficient Gibbs Sampling Algorithm for Bayesian Graphical LASSO Models with the Positive Definite Constraint on the Precision Matrix
Wang (2012) proposed a novel Gibbs sampling algorithm for Bayesian analysis of Gaussian graphical LASSO models. In this paper, we propose a modification to Wang(2012)'s algorithm so that the precision matrix in a graphical LASSO model would never fail to be positive definite in every cycle of the Gibbs sampling procedure. Our proposed algorithm is designed to sample the off-diagonal elements of the precision matrix exactly from the region where the precision matrix remains positive definite. As a result, it is more stable in the sense that the sampling procedure will not halt due to numerical exceptions related to the lack of positive definiteness. The simulation results show that our proposed algorithm can significantly improve the performance of parameter estimation and graphical structure learning.
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